Astroquizzical

When a particle moves through spacetime, how do we know it is the same particle and not some excitation that is passed from place to place?

Wispy tendrils of hot dust and gas glow brightly in this ultraviolet image of the Cygnus Loop Nebula, taken by NASA’s Galaxy Evolution Explorer. The nebula lies about 1,500 light-years away, and is a supernova remnant, left over from a massive stellar explosion that occurred 5,000-8,000 years ago. Image credit: NASA/JPL-Caltech

We don’t! This is a really interesting feature of our universe, and it comes from the observation that all subatomic particles are described by a few key properties, but are otherwise completely and utterly identical. Electrons appear to be identical to all other electrons. All photons (if they carry the same energy within them) are identical to all other photons of that energy. Protons are identical to other protons, and neutrons are identical to other neutrons. All of these particles are distinguished from each other by their mass, electric charge, and a property called their spin. However, each and every single electron in the Universe has the exact same mass, electric charge, and spin. There are no other measurements we can do to distinguish a given electron from another.

We could think of it along these lines: let’s say I give you a ping pong ball, and tell you that this one is special because it’s yours. But then we throw that ping pong ball into a bag full of other balls which look just like yours and mix them up. It’d be quite difficult to tell if the one I pull out of the bag next is the one I initially gave you or another one. If that newly drawn ball is identical in all measurable ways to the original one I told you was yours, there’s really no way to tell if it’s the one I originally handed to you or not.

Photons have one extra parameter that can distinguish them from each other and it’s the amount of energy they’re carrying. This energy corresponds to the color of the light - the more energy, the further to the blue the light appears, and the less energy, the harder to the red it falls. I can distinguish a blue photon from a red one as it hits my camera because of this difference in energy, but the mass, electric charge, and spin of those two photons are the same.

If the photons have the same energy when they arrive, then I’ve run out of ways to distinguish them.

So if I dump a bunch of photons into my metaphorical bag, and they all come out again, there’s no way for me to tell if my favorite photon came out first or last. The closest astrophysical approximation to this simple setup is light which strikes the surface of the Sun and is then absorbed. That photon is now mixing with a huge number of other photons created within the depths of the Sun, and I have no way of flagging that particular photon to distinguish it from the flood of other, identical photons which are streaming outwards away from the Sun.

The energy that a photon carries isn’t a fundamental property of the photon in the way that its electric charge (which is neutral) and its spin are fundamental properties. Fundamental properties cannot be changed, no matter what happens to these photons in the course of bouncing around the Universe. So the energy of a photon, not being a fundamental property, canbe changed. And this energy often is changed, making our attempt to keep track of individual photons even more difficult. The photons that stream from the Sun and onto the surface of the Earth deposit some of their energy into the matter of the Earth, heating up the ground. That heating process depletes the energy remaining in the photon, and so the photon which reflects away has changed the amount of energy that it carries with it. So, if I see photons streaming into a region of space where they must interact with other objects, the identities of individual photons are even more scrambled than they would have been while they were streaming freely through space.

Your idea of energy excitations passing from place to place is precisely the right one for fundamental particles - nothing we can measure will tell me which electron is my favorite.